Understanding fluid domain

Hello, I think I have a conceptual misunderstanding of what a domain means for fluid simulation.
I have set up a sphere as fluid, and the two cubes connected by the cylinder as the fluid domain:

However, when I bake it, the fluid does not respect the boundaries of the domain, it simply falls down as if the domain did not contain the narrow drain, but as if it was a simple cube.
How can I make the fluid flow through the narrow cylinder?
Thank you



The object you are using as the domain should be set to be an obstacle. The domain is a cube in which the whole fluid simulation exists